Find the Exact Value sec(58)

Problem

sec(58)

Solution

1. Identify the expression as the secant of an angle measured in degrees.

2. Recognize that 58 is not a standard reference angle (such as 0,30,45,60,90.

3. Apply the reciprocal identity for secant, which states that sec(θ)=1/cos(θ)

4. Determine if the value can be expressed using radicals via sum or difference formulas. Since 58 is not a multiple of 3 it cannot be expressed in terms of basic square roots.

5. Conclude that the exact value is represented by the trigonometric expression itself or its reciprocal form.

Final Answer

sec(58)=1/cos(58)

Want more problems? Check here!